GIDA (2014) 39 (3): 131-138 doi: 10.5505/gida.65265
GD13066
Research / Araflt›rma
MATHEMATICAL MODELING and THIN LAYER DRYING of CHICKEN MEAT ENRICHED BAGUETTE BREAD SLICES Hülya Çakmak1*, Seher Kumcuoğlu2, Şebnem Tavman2 1
Ege University, Graduate School of Natural and Applied Sciences, Department of Food Engineering, Izmir, Turkey 2 Ege University, Faculty of Engineering, Department of Food Engineering, Izmir, Turkey Received / Gelifl tarihi: 24.10.2013 Received in revised form /Düzeltilerek Gelifl tarihi: 14.01.2014 Accepted / Kabul tarihi: 24.02.2014
Abstract The aim of this study is to determine thin layer drying behaviour of chicken meat powder (CMP) and chicken meat (CM) enriched baguette bread slices at 170, 190 and 210 °C in a convection oven for production of two new snacks. Only falling-rate period was observed for both of the snacks, however only for 10%-CMP enriched sample at 170 °C drying had a constant-rate period as well. Nine different mathematical models were fitted to experimental drying data and those tested models were compared based on the model selection criteria (highest adj-R2, lowest F2 and RMSE) by using nonlinear regression analysis. Midilli et al. model was determined as the best model among all for predicting the moisture ratios of baguette slices with respect to time. Effective diffusion coefficient was found between 5.471x10-8-8.308x10-8 m2/s for CMP enriched baguettes, while it was between 4.458x10-8-7.498x10-8 m2/s for CM enriched baguettes. Also mathematical expressions were defined to explain the temperature dependency of effective diffusion coefficients.. Keywords: Drying, mathematical modeling, diffusion, activation energy
TAVUK ETİYLE ZENGİNLEŞTİRİLMİŞ BAGET EKMEĞİ DİLİMLERİNİN İNCE TABAKA KURUTULMASI ve MATEMATİKSEL MODELLEMESİ Özet Bu çal›flman›n amac›, tavuk eti unu (CMP) ve tavuk eti (CM) ile zenginlefltirilmifl baget ekme¤i dilimlerinin 170, 190 ve 210 °C’de konveksiyonlu f›r›nda ince tabaka kurutulmas› ve yeni iki at›flt›rmal›k çerez üretilmesidir. Tüm çerezler için kuruma ifllemi yaln›zca azalan ak› bölgesinde gerçekleflirken, %10-CMP ile zenginlefltirilen çerezlerin 170 °C’de kurutulmas›nda azalan ak›n›n yan› s›ra sabit ak› bölgesi de gözlemlenmifltir. Dokuz farkl› kuruma modeli deneysel kuruma verilerine uygulanm›fl ve verilen modeller model seçim ölçütüne göre (en yüksek düzeltilmifl belirleme katsay›s› ile en düflük indirgenmifl ki-kare ve en düflük kök ortalama kare hatas›) do¤rusal olmayan regresyon analizi uygulanarak karfl›laflt›r›lm›flt›r. Midilli et al. modelinin, verilen modeller aras›nda baget dilimlerinin zamana ba¤l› nem oran›n› tahminlemekte en iyi model oldu¤u görülmüfltür. Etkin difüzyon katsay›s› CMP ile zenginlefltirilen örnekler için 5.471x10-8-8.308x10 -8 m 2/s aras›nda de¤iflirken, CM ile zenginlefltirilen örneklerde 4.458x10-8-7.498x10-8 m2/s aras›nda oldu¤u bulunmufltur. Ayr›ca etkin difüzyon katsay›s›n›n s›cakl›¤a ba¤›ml›l›¤›n› gösteren matematiksel eflitlikler tan›mlanm›flt›r. Anahtar kelimeler: Kurutma, matematiksel modelleme, difüzyon, aktivasyon enerjisi *Corresponding author/ Yazışmalardan sorumlu yazar
[email protected], ✆ (+90) 232 388 2395,
(+90) 232 342 7592
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H. Çakmak, S. Kumcuoğlu, Ş. Tavman
INTRODUCTION Increasing life standards impose people to change their eating habits and promote them to consume unhealthy, high energy, high fat, and sugar containing fast foods and snacks. It was stated that 30.3% of people reported that they are consuming fast food on a typical day (1). But appropriate snacking can help to maintain healthy body weight and encourage people for consumption of healthy choices on daily diet (2). Also certain populations in the world may not be receiving adequate levels of nutrients, may be experiencing nutritional deficiencies, and may be in environments in which disease or other adverse conditions affect their metabolic states (3). For eliminating these negative effects, some strategies are developed, such as enrichment of frequently consumed foods to regulate the nutrient intake in daily diet. Especially increasing protein content of widely consumed bread is one of the major concerns in most researches (4-7). However these types of enriched breads are susceptible to chemical, physical, and sensorial deteriorations as well as microbiological instabilities with their high moisture contents (up to 40%). Removal of that excess water from food can help to give a longer shelf life without any spoilage and increase stability of food during storage (8). Drying is one of the oldest food preservation methods for decreasing available water in food materials and increasing shelf life of foods. This process involves simultaneous heat and mass transfer, however due to the complexity of this process, some researchers developed semitheoretical models derived from Fickian diffusion approach to explain the water movement within the solid food materials (9). In these models, thin layer structure is assumed to simplify the Fick’s second law and based on the solution of partial differential equations, extensive body of literature has been arisen for demonstrate the theoretical drying of several agricultural materials and food products. However the high energy intensity of drying process encourages food scientists to understand, model and optimize the whole process for each of new developed foodstuffs. The objectives of this study is to produce new, rusk like, protein enriched snacks by adding chicken meat powder and chicken meat into baguette bread formulations and determine the
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drying mechanism of these snacks with increasing drying temperature. Also thin layer modeling of the drying process to predict and simulate the drying behaviour of these new snacks was studied. For this purpose, nine different thin layer drying models were fitted to experimental drying data and applicability of the models was compared according to statistical parameters.
MATERIALS and METHODS Materials The white wheat flour (type 650) was obtained from Yuksel Tezcan Gida A.S. (Turkey). The industrial chicken meat powder and raw whole chicken were supplied from Banvit A.S. (Turkey) and Keskinoglu A.S. (Turkey), respectively. EMCE gluten plusP baking improver (ABP Mühlenchemie A.S., Turkey) with a rate of 0.3% (on flour basis) were blended with dry ingredients. Other ingredients were obtained from a local market. Production of Chicken Meat Enriched Baguette Breads The raw whole chicken was first boiled in tap water until its cold point temperature exceeds 70 °C. Then skin and the bones were removed and the cooked chicken meat was grounded into small pieces in a blender (Waring Blender, USA) to produce final chicken meat enrichment source. The bread production was optimized using traditional French baguette processing as stated in the study of Baardseth et al. (10) with slight modifications. The level of chicken meat powder (CMP) and chicken meat (CM) - between 0-30% were determined from a series of sensory analysis. At the first step of sensory analysis, there was no statistical difference observed (P0.99), however parabolic model with its comparably low correlation coefficient was insufficient to represent the drying data. But according to the model selection criteria, the highest adj-R2, with the lowest F2 and RMSE values were obtained for Midilli et al. model. Also the goodness of fit can be seen in Figure 3 and 4 with respect to time. This model is very successful for explaining drying kinetics of various agricultural and food products (29-31). Figure 2. Experimental drying curves of 10%-CM enriched baguette slices at 170 °C (o), 190 °C (F), 210 °C (∆).
Mathematical Modeling of Drying The moisture contents of samples were transformed into dimensionless moisture ratio to perform modeling studies easily. The experimental moisture ratios were fitted to mathematical models shown in Table 2. These models were fitted to experimental data and obtained drying constants, adj-R2, F 2 and RMSE are presented in Table 3 and 4. Those constants given in the tables will help the researchers to predict the drying behaviour of a similar food material without doing any experimental studies.
The comparison of the experimental and Midilli et al. predicted moisture ratios were shown in Figure 5 and 6. The predicted values were accumulated around a straight line, which was a strong proof of the chosen models suitability (24). Effective Diffusion Coefficient and Activation Energy Effective diffusion coefficients were calculated from Eq. 7, and the values of 10%-CMP enriched baguette slices were found as 5.471x10 -8 , 6.181x10-8, and 8.308x10-8 m2/s at 170, 190, and 210 °C drying temperatures, respectively. The effective diffusion coefficients of 10%-CM enriched baguette slices were found as 4.458x10 -8 , 5.775x10-8, 7.498x10-8 m2/s at 170, 190, and 210 °C
Table 3. Model parameters and statistical results of thin layer drying of 10%-CMP enriched baguette slices Model Temperature Model constants no (°C) 1
2
3
4
5
6
7
8
9
170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210
k=0.004391 k=0.005615 k=0.006403 a=1.045, k=0.004549 a=1.025, k=0.005726 a=1.020, k=0.006500 a=0.4704, k=0.004547, b=0.2837, g=0.004531, c=0.2891, h=0.004549 a=0.3143, k=0.005717, b=0.3967, g=0.005733, c=0.3136, h=0.005717 a=0.3335, k=0.006494, b=0.3792, g=0.006512, c=0.3063, h=0.006487 a=1.056, k=0.004381, c= -0.0138 a=1.032, k=0.005596, c= -0.008187 a=1.032, k=0.006262, c= -0.01334 k=0.004908, n=0.9783 k=0.01486, n=0.8202 k=0.01558, n=0.8364 a=3.097, k0=0.003667, b= -2.06, k1=0.003306 a=4.284, k0=0.004009, b= -3.263, k1=0.003607 a= 3.854, k0=0.01119, b= -2.859, k1=0.01506 a=2.052, k=0.006854 a=2.004, k=0.008522 a=2.071, k=0.009926 a=0.7962, b= -0.001495, c=6.242x10-7 a=0.7396, b= -0.001525, c=6.913x10-7 a=0.825, b= -0.00229, c=1.415x10-6 a=0.9997, k=0.0002916, n=1.483, b=1.429x10-6 a=0.9998, k=0.0006441, n=1.401, b=1.788x10-6 a=1.00, k=0.0006688, n=1.428, b=1.894x10-6
adj-R2
F2
RMSE
0.9833 0.9902 0.9904 0.9841 0.9901 0.9898 0.9777 0.9857 0.9816 0.9843 0.9899 0.9898 0.9800 0.9736 0.9763 0.9849 0.9922 0.9998 0.9994 0.9997 0.9998 0.8424 0.7838 0.8553 0.9998 0.9998 0.9999
0.00146 0.00081 0.00099 0.00139 0.00082 0.00105 0.00195 0.00118 0.00190 0.00137 0.00083 0.00106 0.00175 0.00218 0.00245 0.00133 0.00064 0.00002 0.00005 0.00003 0.00002 0.01382 0.01783 0.01491 0.00002 0.00002 0.00001
0.03825 0.02846 0.03150 0.03735 0.02859 0.03246 0.04420 0.03437 0.04356 0.03706 0.02888 0.03251 0.04188 0.04667 0.04945 0.03645 0.02535 0.00442 0.00707 0.00529 0.00410 0.11760 0.13350 0.12210 0.00428 0.00390 0.00306
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H. Çakmak, S. Kumcuoğlu, Ş. Tavman Table 4. Model parameters and statistical results of thin layer drying of 10%-CM enriched baguette slices Model Temperature Model constants no (°C) 1
2
3
4
5
6
7
8
9
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170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210 170 190 210
k=0.005096 k=0.006811 k=0.007435 a=1.015, k=0.005158 a=1.025, k=0.006936 a=1.021, k=0.007543 a=0.3382, k=0.005159, b=0.3382, g=0.005158, c=0.3382, h=0.005158 a=0.3416, k=0.006935, b=0.3416, g=0.006935, c=0.3416, h= 0.006934 a=0.3406, k=0.007533, b=0.3406, g=0.007529, c=0.3406, h=0.007584 a=1.017, k= 0.005111, c= -0.003058 a=1.03, k=0.006827, c= -0.005713 a= 1.03, k=0.007341, c= -0.009954 k=0.00649, n=0.9428 k=0.01855, n=0.8098 k=0.01742, n=0.8175 a=1.069, k0=0.005152, b= -0.05693, k1=0.005208 a=1.010, k0=0.006939, b=0.01462, k1=0.006491 a=1.019, k0=0.007524, b=0.000011, k1=0.009868 a=0.8131, k=0.005305 a=1.00, k=0.006812 a=1.088, k=0.007488 a=0.7094, b= -0.00127, c=5.031x10-7 a=0.7146, b= -0.001609, c=7.911x10-7 a=0.7886, b= -0.002253, c=1.414x10-6 a=0.9991, k=0.001863, n=1.183, b=1.766x10-6 a=1.001, k=4.96x10-5, n=1.963, b=4.553x10-6 a=1, k=5.31x10-5, n=1.974, b=5.588x10-6
adj-R2
F2
RMSE
0.9966 0.9771 0.9790 0.9966 0.9759 0.9772 0.9954 0.9638 0.9590 0.9965 0.9740 0.9752 0.9914 0.9598 0.9559 0.9961 0.9710 0.9707 0.9963 0.9752 0.9767 0.7802 0.7208 0.7848 0.9992 0.9948 0.9977
0.00025 0.00193 0.00214 0.00025 0.00214 0.00232 0.00034 0.00306 0.00418 0.00026 0.00220 0.00253 0.00063 0.00340 0.00450 0.00029 0.00245 0.00299 0.00027 0.00209 0.00237 0.01617 0.02359 0.02195 0.00006 0.00044 0.00024
0.01571 0.04396 0.04624 0.01574 0.04516 0.04821 0.01838 0.05531 0.06469 0.01607 0.04688 0.05034 0.02511 0.05828 0.06710 0.01692 0.04947 0.05467 0.01657 0.04576 0.04871 0.12720 0.15360 0.14820 0.00789 0.02090 0.01540
drying temperatures, respectively. Those values were calculated with high multiple correlation coefficients, and they were R2>0.94 for 10%-CMP enriched and R2>0.99 for 10%-CM enriched baguette slices. Above given values are consistent with the other agricultural and food products that are reviewed by Erbay and Icier (9). It was stated by Chen (13) that, the diffusivity of bread having moisture content between 0.1-0.75 kg water/kg dry matter were given between 2.8x10 -9 to 9.6x10-7 m2/s while Tong and Lund (32) found
between 2.5x10-9 to 5.5x10-7 m2/s for bread having moisture of 0.1-0.7 kg water/kg dry matter for temperatures between 20-100 °C, which are consistent with our present study. Xu and Kerr (28) reported slightly lower values for tortilla chips for comparably low drying temperatures; however the structure of the tortilla chips were probably different than our samples which influences the moisture distribution and movement inside the material, and so changing the mechanism of drying.
Figure 3. Variation of experimental and Midilli et al. predicted MRs of 10%-CMP enriched baguette slices at 170 °C (o), 190 °C (F), and 210 °C (∆).
Figure 4. Variation of experimental and Midilli et al. predicted MRs of 10%-CM enriched baguette slices at at 170 °C (o), 190 °C (F), and 210 °C (∆).
Mathematical Modeling and Thin Layer Drying... This shows that temperature sensitivity of the activation energy of CM enriched baguette bread slices were higher than the CMP enriched baguette bread slices. These values are rather lower than the values for bread, biscuit and muffin where the diffusion coefficient dependency expressed as a function of both temperature and moisture content (32).
CONCLUSION Figure 5. Experimental versus predicted MRs of 10%-CMP enriched baguette slices at 170 °C (o), 190 °C (F), 210 °C (∆).
Figure 6. Experimental versus predicted MRs of 10%-CM enriched baguette slices at 170 °C (o), 190 °C (F), 210 °C (∆).
As effective diffusion coefficients are strongly correlated with drying temperature, Xanthopoulos et al. (33) were suggested developing a mathematical model to relate the temperature dependency, treating the effective diffusion coefficient as the dependent variable and temperature as the independent variable. The following expressions were determined according to aforementioned study for both of the baguette samples by regression analysis; Deff (CMP) = 5.984 x 10-5 exp (–3166/T)
(9)
Deff (CM) = 2.433 x 10 exp (–2795/T)
(10)
-5
where T refers to the drying temperature (K). Adj-R 2 and RMSE were found as 0.8846 and 5.015x10-9 for CMP enriched baguettes, while for CM enriched baguettes they were 0.9986 and 5.791x10-10. Those values testify the accuracy of derived expressions. The activation energies were calculated as 18.47 kJ/mol for CMP enriched samples, and 23.12 kJ/mol for CM enriched samples, respectively.
The thin layer drying behaviour of chicken meat powder and chicken meat enriched baguette bread slices at 170, 190 and 210 °C in convection oven were studied. The samples had reached the equilibrium moisture contents (0.031 and 0.040 g water/g dry matter) between 20-32 min. Only falling-rate period was observed for all samples; however 10%-CMP enriched sample at 170 °C drying had a constant-rate period as well. Drying rate was significantly affected by increasing drying temperatures. Nine different mathematical models were tested and, Midilli et al. model was found satisfactory to represent the drying behaviour of these snacks. Also depending on the activation energies, chicken meat enriched samples were found to be more heat sensitive than chicken meat powder enriched samples. ACKNOWLEDGEMENT This research is fully funded by TUBITAK with project no: 110-O-030.
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